Empirical Approach for Optimal Reinsurance Design

This paper proposes a novel and practical approach of addressing optimal reinsurance via an empirical approach. This method formulates reinsurance models using the observed data directly and has advantages including (i) transformation of an infinite dimensional optimization problem to finite dimension, (ii) no explicit distributional assumption on the underlying risk is required, and (iii) many empirical-based reinsurance models can be solved efficiently using the second-order conic programming. This allows insurers to incorporate many desirable objective functions and constraints while still retaining the ease of obtaining optimal reinsurance strategies. Numerical examples, including applying to an actual Danish fire loss data, are provided to highlight the efficiency and the practicality of the proposed empirical models. Stability and consistency of the empirical-based solutions are also analyzed numerically